Big Idea:
Are your students still counting to do 10 more? This lesson helps them explore how the numbers change when they repeatedly add 10 and why they change, helping push them towards mental math!

In first grade, the CCSS (1.NBT.C5) asks that students be able to mentally find 10 more or 10 less then a given number. It specifically states that students should not have to count, but that they also should be able to explain the reasoning used. The Common Core also emphasizes that students have a conceptual understanding, which means they learn math without having to learn "tricks". In this lesson, students explore how numbers change when they repeatedly add 10. This sets students up to later understand how to mentally find 10 more.

Students also apply MP7 and MP8 throughout this lesson. Students notice the structure of the number and then use repeated reasoning to help themselves solve future problems.

Review Past Learning:

We have worked with 10 all year. 10 is our best friend! Today we are going to look at another way we can use 10-by adding 10 over and over.

Connect to the Real World:

This is important because grown ups use adding 10 to help them add things quicker. For example, if I have $24, and then I get $10, I don't count on to figure out how much money I have. I use what I know about adding 10s to make it easier to solve.

Objective:

Your thinking job today is: How does the number change when I add 10 over and over?

Present Task: Today we are going to enter the world of Woody and Buzz. Andy, their owner, is getting a bunch of new toys, but only if he does his chores. He gets 10 new toys everyday! We are going to figure out how many toys he has at the end of every day.

Problem 1: Andy has 15 toys in his toy box. He gets 10 more on Monday for doing his chores. How many toys does he have now?

Retell what happened in the story.

Predict: Will Andy have the same number of tens or ones after he gets his new toys?

This question helps students start to look for repeated reasoning (CCSS MP8). We are going to ask this question every time Andy gets 10 more. I want students paying attention to how the place value of each new number is the same and different as the starting number-this will help them see that only the 10s place is changing.

I'll choose one person to come and model this problem with base 10 blocks. Other students will get to solve later!

After student solves, and we record the answer, 25, I'll ask: Does Andy have the same number of 10s or 1s in his new amount of toys? Look closely at 15 and 25-what is the same about these 2 numbers?

Problem 2: Now Andy gets 10 more on Tuesday for doing his chores. How many toys does he have now?

What number are we starting with? Will we start with the 15 he had at first? Why not?

Predict: Will Andy have the same number of tens or ones after he gets his new toys?

Partner solve: I'll give students base 10 blocks to show how to solve this problem.

I'll choose one person to share how many we had now! Watch this Student Model to see how one child explained it. After student solves, and we record the answer, 35, I'll ask: Does Andy have the same number of 10s or 1s in his new amount of toys?

More than likely, a child will present 45 as a prediction. This prediction is the focus of the discussion.

Guiding Questions:

Why would 45 come next?

Scaffold: What is happening in the first 3 numbers: 15, 25, 35 that makes you think 45 will come next?

How can we prove that 45 will come next?

This question has 2 major benefits: students have to construct a viable argument to prove to their peers that 45 will come next (MP3). They also have to choose an appropriate tool and use it strategically to prove their thinking is correct (MP5). Most students will prove it with base 10 blocks, but others might think about how this looks on the number line, hundreds chart or even prove it with mental counting.

Prove it! I'll have one student show how they are sure 45 comes next.

Partner talk to summarize: Why did 45 come next in this group? How did the numbers change in this chart: 15, 25, 35, 45?

Resources (2)

Resources

Students get a start number (decided and written in by teacher) to start with. They use the Toy Box mat for their base ten models and show how Jack gets 10 more toys every day.

Group A: Intervention

This group should start with a number under 10. These students also need to scaffold of base 10 blocks throughout. They may revert back to adding 10 ones. If that is the case, I'll ask: Is there another way we could represent 10?

Group B: Right on Track

Students get a number in the teens to start with. They have base ten blocks available.

Group C: Extension

Students start with a number in the twenties. They have base ten blocks available, but they may be able to do this mentally. If that is the case, make sure they can explain the reasoning of how they figured out 10 more, as this is explicitly stated in the standard.

One of the strategies I sometimes get is "I went down on the hundreds chart"-while this does work, I want to always make sure students have a conceptual understanding of why "going down" on the chart works. To scaffold this conversation, I'll ask: What is happening to the number when you move down the hundreds chart? How does that show you are adding 10?

I saw a variety of strategies from students during this activity. I listed them below-click on the link to see the picture of a student using that strategy. I listed the strategies from most concrete (students use concrete models to solve) to most abstract.

Base 10: Students take out the appropriate number of base 10 blocks and physically move them to the group.

I'll close the lesson by having students apply what they did today to a novel problem. This is just an equation-no story attached to it. Students are asked to show 2 strategies to solve 48 + 10. The 2 strategies is intentional-I am hoping students will show the pattern that they saw in today's lesson as one of their strategies. I am anticipating that the other strategy they will show will use a base 10 model.

This problem also gives me some data to use as I differentiate for the next day's lesson.